On the GRE, Select One or More questions use square checkboxes instead of round radio buttons — signaling that multiple answers may be correct. There is no partial credit: you must select every correct answer and only correct answers. The algebra questions in this format test sufficiency reasoning, must-be-true identities, sign analysis, and work-rate problems. Below you will learn the three main question patterns, work through two interactive walkthroughs step by step, and then practice with questions drawn from the official question bank.
What Are Select One or More Algebra Questions?
In the GRE Quantitative Reasoning section, Select One or More questions present you with a problem and several answer choices marked by square checkboxes. One or more of the choices may be correct. You receive credit only if you select all the correct answers and none of the incorrect ones. There is no partial credit — missing one correct answer or including one wrong answer means zero points for that question.
When the content domain is algebra, these questions typically involve equations, inequalities, expressions with unknowns, work-rate problems, or sufficiency reasoning. The algebra is usually straightforward, but the challenge lies in evaluating each choice independently and avoiding the trap of combining information across choices when the question asks about each one individually.
Format cue: Square checkboxes mean "select all that apply." Round radio buttons mean "select exactly one." On the real GRE, this visual distinction is your first signal about how many answers may be correct. Never assume only one answer is right when you see checkboxes.
Three Question Patterns You Will See
Nearly every Select One or More algebra question follows one of three patterns. Recognizing the pattern tells you immediately what strategy to apply.
1
Sufficiency Questions
'Which of the following statements individually provide sufficient additional information to determine [some quantity]?' You test each statement in isolation with the given setup. If a statement allows you to solve for the unknown uniquely, it is sufficient.
2
Must Be True Statements
Given algebraic constraints (such as ranges, positions on a number line, or relationships between variables), determine which of several algebraic statements must hold in every case. You must verify each statement for all possible values, not just one example.
3
Value Satisfaction Questions
'Which of the following values of x satisfy [some condition]?' or 'For which values of k does the equation have [some property]?' You test each choice by substitution or algebraic reasoning to determine which values work.
How to Solve These Questions Step by Step
These five strategies apply across all three patterns. They are ordered to match the natural flow of problem solving on this question type.
Before looking at the answer choices, define your variables, write down all equations from the problem setup, and identify how many unknowns remain. For sufficiency questions, count the degrees of freedom. For must-be-true questions, express all variables in terms of a single parameter if possible. This upfront work makes evaluating each choice faster and less error-prone.
The most important discipline for Select One or More questions is treating each choice as a standalone problem. For sufficiency questions, pretend you only have the original setup plus the single statement being tested. For must-be-true questions, verify the statement across the full range of allowed values. Never let your analysis of choice A influence your thinking about choice B.
Some problems contain constraints that are not immediately obvious. In work-rate problems, rates are additive when working simultaneously. In tiered commission structures, reaching a higher tier forces all lower tiers to their maximum. In number-line problems, the spacing between tick marks is constant and positive. These hidden constraints often make a statement sufficient when it first appears insufficient.
When a statement seems borderline, try to construct two different scenarios consistent with the statement. If both scenarios give the same answer, the statement is likely sufficient (or the algebraic claim is likely true). If they give different answers, the statement is not sufficient (or the claim is false). This technique catches errors in abstract reasoning.
Unlike standard multiple choice where exactly one answer is correct, Select One or More questions may have any number of correct answers — one, two, three, or even all of them. After finding one correct choice, continue evaluating every remaining choice with the same rigor. Stopping early is the most common cause of lost points on this format.
Pro tip: On sufficiency questions, a statement is sufficient if and only if it reduces the degrees of freedom to zero — meaning the unknown quantity has exactly one possible value. If even two possible values remain, the statement is not sufficient.
Worked Example: Quadratic Inequality
This walkthrough covers a quadratic inequality problem — a common pattern in Select One or More algebra. The key technique is factoring, finding the sign intervals, and testing each choice. Work through each step below.
Interactive Walkthrough0/4 steps
Integer Solutions of a Quadratic Inequality
Find all integer values of x from the choices below for which x2−7x+10≤0.
Which of the following integers satisfy the inequality? Indicate all such integers.
0
2
3
5
7
1
Step 1: Factor the quadratic
x2−7x+10=(x−2)(x−5). What are the roots?
2
Step 2: Determine the sign pattern
3
Step 3: Test each choice
4
Step 4: Verify a boundary value
Worked Example: Values of k for Real Roots
This walkthrough covers a discriminant problem — testing which parameter values produce real roots. The key technique is setting up the discriminant inequality and checking each choice.
Interactive Walkthrough0/4 steps
Values of k for Real Roots
The quadratic equation x2+kx+9=0 has real roots only when the discriminant is non-negative.
For which values of k does the equation have at least one real root? Indicate all such values.
-8
-5
0
6
10
1
Step 1: Write the discriminant
For ax2+bx+c=0, the discriminant is b2−4ac. Here a = 1, b = k, c = 9. What is the discriminant?
2
Step 2: Set up the inequality
3
Step 3: Test each choice
4
Step 4: Check the boundary case k = 6
Practice Questions
Apply what you learned. Each question uses the Select All That Apply format with square checkboxes. After you submit, click through the step-by-step solution to compare against your work. Remember: you must select every correct answer and only correct answers to receive credit.
Question 1 — Quadratic Root Conditions
For which of the following values of k does the equation x2+kx+(k+3)=0 have two distinct positive real roots? Indicate all such values.
Question 2 — Sign Analysis of Expressions
If −1<x<0, which of the following expressions must be negative? Indicate all such expressions.
Question 3 — Algebraic Identities
If a and b are real numbers such that a2+b2=25 and ab=12, which of the following statements must be true? Indicate all such statements.
Question 4 — Rational Inequality
Which of the following values of x satisfy the inequality x2−9x2−4≤0? Indicate all such values.
Question 5 — System of Equations with No Solution
For which of the following values of m does the system 2x+my=4, mx+8y=m have no solution? Indicate all such values.
Question 6 — Quadratic with Integer Roots
If the quadratic equation x2−(k+3)x+(2k+2)=0 has two integer roots, which of the following could be the value of k? Indicate all such values.
Question 7 — Absolute Value Inequality
For which of the following values of a does the inequality ∣x−3∣+∣x+1∣≤a have a non-empty solution set? Indicate all such values.
Question 8 — Function Composition Inequality
Let f(x)=x2−6x+8 and g(x)=2x−1. Which of the following values of x satisfy f(g(x))<0? Indicate all such values.
Four Common Traps
Trap 1 — Combining statements in sufficiency questions. When a question asks which statements "individually provide sufficient information," each statement must be evaluated in isolation. Do not combine the information from statement A with statement B. Each one must work on its own with only the original problem setup.
Trap 2 — Testing only one value for "must be true" questions. If the question asks what must be true for all x in an interval, checking a single value of x is not enough. You must verify the statement algebraically for the entire range, or find a counterexample to disprove it. A statement that holds for x=−21 might fail for x=−0.99.
Trap 3 — Confusing strict and non-strict inequalities. When the question uses a strict inequality (less than, greater than), the boundary values where the expression equals zero are not included. When the question uses a non-strict inequality (less than or equal to), boundary values are included. Mixing these up adds or removes one answer choice.
Trap 4 — Stopping after finding one correct answer. In standard multiple choice, you can stop after finding the right answer. In Select One or More, there may be two, three, or even more correct choices. Always evaluate every single choice before submitting.
MCM vs. Standard Multiple Choice
Understanding the structural differences between Select One or More and standard multiple choice helps you adjust your approach.
Feature
Standard MC (Select One)
Select One or More
Visual cue
Round radio buttons
Square checkboxes
Correct answers
Exactly one
One or more (could be all)
Partial credit
N/A (binary)
None — all or nothing
Strategy difference
Eliminate wrong answers, pick the best
Evaluate each choice independently as true/false
Time management
~1.5 minutes
~2-3 minutes (must check every choice)
Common error
Misreading one answer
Missing one correct or including one wrong
The key strategic difference is that Select One or More requires you to think of each choice as an independent true/false proposition. In standard MC, once you find the correct answer you are done. In Select One or More, you must confirm or reject every single choice.
Study Checklist
Select One or More Algebra Mastery Checklist0/8 complete
Frequently Asked Questions
How do Select One or More algebra questions differ from standard multiple choice?
In Select One or More questions, you must identify every correct answer from the choices. There is no partial credit: missing even one correct choice or including one incorrect choice results in zero credit. The choices use square checkboxes instead of round radio buttons. Standard multiple choice has exactly one correct answer and uses radio buttons.
What algebra topics appear most often in GRE Select One or More questions?
The most common topics are sufficiency questions (determining which statements provide enough information to solve a problem), must-be-true algebraic identities, sign analysis of expressions under given constraints, and work-rate problems. These questions frequently test whether you can reason about what information is necessary versus sufficient.
How many correct answers should I expect in a Select One or More question?
There is no fixed number. Some questions have one correct answer, others have two or three, and occasionally all choices are correct. You must evaluate each choice independently based on the mathematics. Never assume a specific number of correct answers — let the algebra determine how many choices are right.
What is the most common mistake on sufficiency-type questions?
The most common mistake is combining information from multiple statements when the question asks which statements individually provide sufficient information. Each statement must be evaluated in isolation with only the original problem setup. A close second is overlooking hidden constraints that make a statement sufficient — for example, in tiered commission problems, the existence of a higher-tier commission automatically maxes out all lower tiers.
How should I handle must-be-true algebra questions?
For must-be-true questions, you need to verify that a statement holds for every possible value satisfying the given constraints, not just one example. Use algebraic identities and sign analysis rather than testing a single number. If you can find even one counterexample where a statement fails, it is not "must be true." Conversely, if you can prove the statement algebraically from the given constraints, it must be true regardless of which specific values you plug in.